Adaptive sliding mode reliable control for switched systems with actuator degradation

The problem of sliding mode control is considered for a class of uncertain switched systems subject to actuator faults. It is assumed that there may happen degradation in each actuator channel. Besides, the authors relax the restrictive assumption that each subsystem shares the same input channel, which is different from some existing works. In this work, a weighted sum approach of the different input matrices is introduced to construct a common sliding surface. Moreover, by on-line estimating the loss of effectiveness of the actuators, an adaptive sliding mode controller is designed. This does not only compensate the effects of the actuator degradation effectively, but can also reduce the conservatism compared with some existing approaches which only utilise the bound of the gain variation. It is shown that the reachability of the specified sliding surface can be ensured, and a sufficient condition on the exponential stability of sliding mode dynamics is obtained via the average dwell time method. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.